Given $(A \vee B) \vee C = A \vee B \vee C = A \vee (B \vee C)$ is true because of the associative law of linear algebra. I have a question about this rule in the case of a negative.
I have: $\neg(A \vee (B \wedge C)) \vee (B \wedge C)$
Treating the $(B \wedge C)$ as a single term, am I correct to apply the associative rule in this case resulting in $\neg A \vee ((B \wedge C) \vee (B \wedge C))$?
Checking my intial expression with the resulting one with an online simplifier tells me they are both equal, but I am not sure why that is.